Everton continued their mini revival after a deserved 2-1 Carabao Cup win at Aston Villa.
James Garner’s first Toffees goal and Dominic Calvert-Lewin’s strike fired the visitors into the fourth round.
Boubacar Kamara’s late strike gave the scoreline a flattering look after Everton bossed much of the game against their disappointing hosts.
Villa routed the Toffees 4-0 in the Premier League last month but Sean Dyche’s side have begun to mount their recovery following a wretched start.
Successive victories for the first time under Dyche – and first for a year – will continue to rouse the Toffees. With Luton and Bournemouth next to visit Goodison Park there is the chance to find real momentum.
For Villa, whose last major trophy was the 1996 League Cup, it was another disappointing night for a club which so desperately wants to challenge the elite.
They will continue to remain on the fringes with similar performances as they strive for consistency, having won 1-0 at Chelsea on Sunday.
James Garner celebrates after scoring against Aston Villa
There was never any sign Unai Emery’s side would build on that result during a sloppy display where they were outfought and overpowered.
Youri Tielemans’ half-volley landed on the roof of the net after seven minutes but that was as good as it got in the first half.
Everton quickly found a tempo which the hosts struggled with and one which, ultimately, forced a 15th-minute opener.
Robin Olsen was put under pressure and his poor clearance landed kindly for Amadou Onana on the edge of the area, before Calvert-Lewin and Arnaut Danjuma worked the ball back to him.
Boubacar Kamara scored Aston Villa’s reply
The midfielder then clipped a cute ball through to Garner to lash in from 10 yards with the Villa defence static.
They looked ropey and anxious for the rest of the half as the hosts failed to clear their lines and were unnerved by Everton’s pressing and Danjuma’s direct running.
Only an outstanding reflex save from Olsen stopped John McGinn slicing into his own net six minutes before half time after another Danjuma burst embarrassed Ezri Konsa and Matty Cash.
Two minutes later the goalkeeper denied Calvert-Lewin as he tried to round him, the striker putting the rebound wastefully into the sidenetting.
It was a let-off and one Villa should have capitalised on but Jhon Duran fired wildly over in stoppage time to sum up their wayward first half.
Unsurprisingly Unai Emery had seen enough, replacing Duran, McGinn and Leander Dendoncker with Ollie Watkins, Kamara and Lucas Digne at the break.
But it did nothing to improve the hosts and they self destructed five minutes after the restart.
There was little pressure on Tielemans 40-yards out but his pass sold Konsa short and Calvert-Lewin nipped in to streak clear and roll past the exposed Olsen.
A smart Jordan Pickford save from Moussa Diaby stopped the hosts pulling a goal back immediately but there was no sense of a comeback.
Olsen thwarted Calvert-Lewin just after the hour and it looked like Everton would comfortably see the game out.
Yet, Kamara set up a nervy end with eight minutes left when his deflected strike from 20 yards wrong-footed Pickford to creep in.
The goalkeeper saved from Diaby in stoppage time and Douglas Luiz hooked over during a frantic finish but it was too little, too late.
